Intelligent reflecting surfaces (IRSs) are a promising low-cost solution for achieving high spectral and energy efficiency in future communication systems by enabling the customization of wireless propagation environments. Despite the plethora of research on resource allocation design for IRS-assisted multiuser wireless communication systems, the optimal design and the corresponding performance upper bound are still not fully understood. To bridge this gap in knowledge, in this paper, we investigate the optimal resource allocation design for IRS-assisted multiuser multiple-input single-output systems employing practical discrete IRS phase shifters. In particular, we jointly optimize the beamforming vector at the base station and the discrete IRS phase shifts to minimize the total transmit power for the cases of perfect and imperfect channel state information (CSI) knowledge. To this end, two novel algorithms based on the generalized Benders decomposition (GBD) method are developed to obtain the globally optimal solution for perfect and imperfect CSI, respectively. Moreover, to facilitate practical implementation, we propose two corresponding low-complexity suboptimal algorithms with guaranteed convergence by capitalizing on successive convex approximation (SCA). In particular, for imperfect CSI, we adopt a bounded error model to characterize the CSI uncertainty and propose a new transformation to convexify the robust quality-of-service constraints. Our numerical results confirm the optimality of the proposed GBD-based algorithms for the considered system for both perfect and imperfect CSI. Furthermore, we unveil that both proposed SCA-based algorithms can attain a locally optimal solution within a few iterations. Moreover, compared with the state-of-the-art solution based on alternating optimization, the proposed low-complexity SCA-based schemes achieve a significant performance gain.

翻译：智能反射面（IRS）通过实现无线传播环境的可定制化，为未来通信系统实现高频谱和高能效提供了低成本解决方案。尽管针对IRS辅助多用户无线通信系统的资源分配设计已有大量研究，但其最优设计及相应的性能上界仍未完全明确。为填补这一理论空白，本文研究了采用实际离散相位IRS移相器的IRS辅助多用户多输入单输出系统的最优资源分配设计问题。具体而言，我们联合优化基站的波束成形向量与IRS离散相位，以在完美与不完美信道状态信息（CSI）场景下最小化总发射功率。为此，基于广义Benders分解（GBD）方法分别提出了两种算法，分别获取完美与不完美CSI下的全局最优解。此外，为促进实际部署，我们基于连续凸近似（SCA）方法设计了两种具有收敛保证的低复杂度次优算法。针对不完美CSI，采用有界误差模型刻画信道不确定性，并提出新型转换方法凸化鲁棒服务质量约束。数值结果验证了所提GBD算法在所考虑系统中对完美与不完美CSI场景的最优性。同时，我们揭示两种基于SCA的算法均能在少量迭代内收敛至局部最优解。此外，与基于交替优化的现有方案相比，所提出的低复杂度SCA方案实现了显著的性能增益。